Question

the number of views on a viral video can be modeled by the function $l(t) = 7500(4)^{3t + 3}$. write an equivalent function of the form $l(t) = ab^t$.

Explanation:

Step1: Use exponent rules to split the exponent

We know that \(a^{m + n}=a^m\times a^n\), so we can split \(4^{3t + 3}\) as \(4^{3t}\times4^{3}\).
So \(L(t)=7500\times4^{3t}\times4^{3}\)

Step2: Calculate \(4^{3}\)

\(4^{3}=4\times4\times4 = 64\)
So \(L(t)=7500\times64\times4^{3t}\)

Step3: Simplify \(7500\times64\)

\(7500\times64 = 480000\)

Step4: Rewrite \(4^{3t}\) using exponent rules

We know that \((a^m)^n=a^{mn}\), so \(4^{3t}=(4^{3})^{t}=64^{t}\)
So now we have \(L(t)=480000\times64^{t}\)

Answer:

\(L(t) = 480000(64)^{t}\)